def check_jacobian_det(
transform,
domain,
constructor=at.dscalar,
test=0,
make_comparable=None,
elemwise=False,
rv_var=None,
):
y = constructor("y")
y.tag.test_value = test
if rv_var is None:
rv_var = y
rv_inputs = rv_var.owner.inputs if rv_var.owner else []
x = transform.backward(y, *rv_inputs)
if make_comparable:
x = make_comparable(x)
if not elemwise:
jac = at.log(at.nlinalg.det(jacobian(x, [y])))
else:
jac = at.log(at.abs_(at.diag(jacobian(x, [y]))))
# ljd = log jacobian det
actual_ljd = aesara.function([y], jac)
computed_ljd = aesara.function(
[y], at.as_tensor_variable(transform.log_jac_det(y, *rv_inputs)), on_unused_input="ignore"
)
for yval in domain.vals:
close_to(actual_ljd(yval), computed_ljd(yval), tol)
def check_vectortransform_elementwise_logp(self, model):
x = model.free_RVs[0]
x_val_transf = x.tag.value_var
pt = model.initial_point(0)
test_array_transf = floatX(
np.random.randn(*pt[x_val_transf.name].shape))
transform = x_val_transf.tag.transform
test_array_untransf = transform.backward(test_array_transf,
*x.owner.inputs).eval()
# Create input variable with same dimensionality as untransformed test_array
x_val_untransf = at.constant(test_array_untransf).type()
jacob_det = transform.log_jac_det(test_array_transf, *x.owner.inputs)
# Original distribution is univariate
if x.owner.op.ndim_supp == 0:
assert joint_logpt(
x, sum=False)[0].ndim == x.ndim == (jacob_det.ndim + 1)
# Original distribution is multivariate
else:
assert joint_logpt(
x, sum=False)[0].ndim == (x.ndim - 1) == jacob_det.ndim
a = joint_logpt(x, x_val_transf,
jacobian=False).eval({x_val_transf: test_array_transf})
b = joint_logpt(x, x_val_untransf, transformed=False).eval(
{x_val_untransf: test_array_untransf})
# Hack to get relative tolerance
close_to(a, b, np.abs(0.5 * (a + b) * tol))
def test_simplex_bounds():
vals = get_values(tr.simplex, Vector(R, 2), at.dvector, np.array([0, 0]))
close_to(vals.sum(axis=1), 1, tol)
close_to_logical(vals > 0, True, tol)
close_to_logical(vals < 1, True, tol)
check_jacobian_det(tr.simplex, Vector(R, 2), at.dvector, np.array([0, 0]), lambda x: x[:-1])
def test_simplex_accuracy():
val = np.array([-30])
x = at.dvector("x")
x.tag.test_value = val
identity_f = aesara.function([x],
tr.simplex.forward(x,
tr.simplex.backward(x, x)))
close_to(val, identity_f(val), tol)
def check_transform(transform, domain, constructor=at.dscalar, test=0, rv_var=None):
x = constructor("x")
x.tag.test_value = test
if rv_var is None:
rv_var = x
rv_inputs = rv_var.owner.inputs if rv_var.owner else []
# test forward and forward_val
# FIXME: What's being tested here? That the transformed graph can compile?
forward_f = aesara.function([x], transform.forward(x, *rv_inputs))
# test transform identity
identity_f = aesara.function(
[x], transform.backward(transform.forward(x, *rv_inputs), *rv_inputs)
)
for val in domain.vals:
close_to(val, identity_f(val), tol)
def test_find_MAP_discrete():
tol = 2.0**-11
alpha = 4
beta = 4
n = 20
yes = 15
with Model() as model:
p = Beta("p", alpha, beta)
Binomial("ss", n=n, p=p)
Binomial("s", n=n, p=p, observed=yes)
map_est1 = starting.find_MAP()
map_est2 = starting.find_MAP(vars=model.value_vars)
close_to(map_est1["p"], 0.6086956533498806, tol)
close_to(map_est2["p"], 0.695642178810167, tol)
assert map_est2["ss"] == 14
def check_transform_elementwise_logp(self, model):
x = model.free_RVs[0]
x0 = x.tag.value_var
assert x.ndim == logpt(x, sum=False).ndim
pt = model.initial_point
array = np.random.randn(*pt[x0.name].shape)
transform = x0.tag.transform
logp_notrans = logpt(x,
transform.backward(array, *x.owner.inputs),
transformed=False)
jacob_det = transform.log_jac_det(aesara.shared(array),
*x.owner.inputs)
assert logpt(x, sum=False).ndim == jacob_det.ndim
v1 = logpt(x, array, jacobian=False).eval()
v2 = logp_notrans.eval()
close_to(v1, v2, tol)
def test_find_MAP_discrete():
tol = 2.0**-11
alpha = 4
beta = 4
n = 20
yes = 15
with Model() as model:
p = Beta('p', alpha, beta)
ss = Binomial('ss', n=n, p=p)
s = Binomial('s', n=n, p=p, observed=yes)
map_est1 = starting.find_MAP()
map_est2 = starting.find_MAP(vars=model.vars)
close_to(map_est1['p'], 0.6086956533498806, tol)
assert 'ss' not in map_est1
close_to(map_est2['p'], 0.695642178810167, tol)
assert map_est2['ss'] == 14
def check_transform_elementwise_logp(self, model):
x = model.free_RVs[0]
x_val_transf = x.tag.value_var
pt = model.compute_initial_point(0)
test_array_transf = floatX(np.random.randn(*pt[x_val_transf.name].shape))
transform = x_val_transf.tag.transform
test_array_untransf = transform.backward(test_array_transf, *x.owner.inputs).eval()
# Create input variable with same dimensionality as untransformed test_array
x_val_untransf = at.constant(test_array_untransf).type()
jacob_det = transform.log_jac_det(test_array_transf, *x.owner.inputs)
assert joint_logpt(x, sum=False)[0].ndim == x.ndim == jacob_det.ndim
v1 = joint_logpt(x, x_val_transf, jacobian=False).eval({x_val_transf: test_array_transf})
v2 = joint_logpt(x, x_val_untransf, transformed=False).eval(
{x_val_untransf: test_array_untransf}
)
close_to(v1, v2, tol)
def check_vectortransform_elementwise_logp(self, model, vect_opt=0):
x = model.free_RVs[0]
x0 = x.tag.value_var
# TODO: For some reason the ndim relations
# dont hold up here. But final log-probablity
# values are what we expected.
# assert (x.ndim - 1) == logpt(x, sum=False).ndim
pt = model.initial_point
array = np.random.randn(*pt[x0.name].shape)
transform = x0.tag.transform
logp_nojac = logpt(x,
transform.backward(array, *x.owner.inputs),
transformed=False)
jacob_det = transform.log_jac_det(aesara.shared(array),
*x.owner.inputs)
# assert logpt(x).ndim == jacob_det.ndim
# Hack to get relative tolerance
a = logpt(x, array.astype(aesara.config.floatX), jacobian=False).eval()
b = logp_nojac.eval()
close_to(a, b, np.abs(0.5 * (a + b) * tol))
def test_find_MAP():
tol = 2.0**-11 # 16 bit machine epsilon, a low bar
data = np.random.randn(100)
# data should be roughly mean 0, std 1, but let's
# normalize anyway to get it really close
data = (data - np.mean(data)) / np.std(data)
with Model():
mu = Uniform("mu", -1, 1)
sigma = Uniform("sigma", 0.5, 1.5)
Normal("y", mu=mu, tau=sigma**-2, observed=data)
# Test gradient minimization
map_est1 = starting.find_MAP(progressbar=False)
# Test non-gradient minimization
map_est2 = starting.find_MAP(progressbar=False, method="Powell")
close_to(map_est1["mu"], 0, tol)
close_to(map_est1["sigma"], 1, tol)
close_to(map_est2["mu"], 0, tol)
close_to(map_est2["sigma"], 1, tol)
def test_find_MAP():
tol = 2.0**-11 # 16 bit machine epsilon, a low bar
data = np.random.randn(100)
# data should be roughly mean 0, std 1, but let's
# normalize anyway to get it really close
data = (data-np.mean(data))/np.std(data)
with Model() as model:
mu = Uniform('mu', -1, 1)
sigma = Uniform('sigma', .5, 1.5)
y = Normal('y', mu=mu, tau=sigma**-2, observed=data)
# Test gradient minimization
map_est1 = starting.find_MAP()
# Test non-gradient minimization
map_est2 = starting.find_MAP(fmin=starting.optimize.fmin_powell)
close_to(map_est1['mu'], 0, tol)
close_to(map_est1['sigma'], 1, tol)
close_to(map_est2['mu'], 0, tol)
close_to(map_est2['sigma'], 1, tol)
def check_vals(fn1, fn2, *args):
v = fn1(*args)
close_to(v, fn2(*args), 1e-6 if v.dtype == np.float64 else 1e-4)
def test_accuracy_non_normal():
_, model, (mu, _) = non_normal(4)
with model:
newstart = find_MAP(Point(x=[0.5, 0.01, 0.95, 0.99]))
close_to(newstart["x"], mu,
select_by_precision(float64=1e-5, float32=1e-4))
def test_accuracy_normal():
_, model, (mu, _) = simple_model()
with model:
newstart = find_MAP(Point(x=[-10.5, 100.5]))
close_to(newstart["x"], [mu, mu],
select_by_precision(float64=1e-5, float32=1e-4))
def test_dlogp2():
start, model, (_, sig) = mv_simple()
H = np.linalg.inv(sig)
d2logp = model.fastd2logp()
close_to(d2logp(start), H, np.abs(H / 100.0))
def test_dlogp():
start, model, (mu, sig) = simple_model()
dlogp = model.fastdlogp()
close_to(dlogp(start), -(start["x"] - mu) / sig**2, 1.0 / sig**2 / 100.0)
def test_logp():
start, model, (mu, sig) = simple_model()
lp = model.fastlogp
lp(start)
close_to(lp(start), sp.norm.logpdf(start["x"], mu, sig).sum(), tol)